mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
130 lines
3.1 KiB
C
130 lines
3.1 KiB
C
/*
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Copyright (C) 2014 Fredrik Johansson
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb_poly.h"
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#include "acb_dirichlet.h"
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void
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_acb_poly_zeta_cpx_series(acb_ptr z, const acb_t s, const acb_t a, int deflate, slong d, slong prec)
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{
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ulong M, N;
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slong i, bound_prec;
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mag_t bound;
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arb_ptr vb;
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int is_real, const_is_real;
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if (d < 1)
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return;
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if (!acb_is_finite(s) || !acb_is_finite(a))
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{
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_acb_vec_indeterminate(z, d);
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return;
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}
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if (acb_is_one(s) && deflate && d == 1)
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{
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acb_digamma(z, a, prec);
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acb_neg(z, z);
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if (!acb_is_finite(z)) /* todo: in digamma */
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acb_indeterminate(z);
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return;
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}
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is_real = const_is_real = 0;
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if (acb_is_real(s) && acb_is_real(a))
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{
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if (arb_is_positive(acb_realref(a)))
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{
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is_real = const_is_real = 1;
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}
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else if (arb_is_int(acb_realref(a)) &&
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arb_is_int(acb_realref(s)) &&
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arb_is_nonpositive(acb_realref(s)))
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{
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const_is_real = 1;
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}
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}
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mag_init(bound);
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vb = _arb_vec_init(d);
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bound_prec = 40 + prec / 20;
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_acb_poly_zeta_em_choose_param(bound, &N, &M, s, a, FLINT_MIN(d, 2), prec, bound_prec);
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_acb_poly_zeta_em_bound(vb, s, a, N, M, d, bound_prec);
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_acb_poly_zeta_em_sum(z, s, a, deflate, N, M, d, prec);
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for (i = 0; i < d; i++)
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{
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arb_get_mag(bound, vb + i);
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arb_add_error_mag(acb_realref(z + i), bound);
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if (!is_real && !(i == 0 && const_is_real))
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arb_add_error_mag(acb_imagref(z + i), bound);
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}
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mag_clear(bound);
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_arb_vec_clear(vb, d);
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}
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void
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_acb_poly_zeta_series(acb_ptr res, acb_srcptr h, slong hlen, const acb_t a, int deflate, slong len, slong prec)
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{
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acb_ptr t, u;
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hlen = FLINT_MIN(hlen, len);
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t = _acb_vec_init(len);
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u = _acb_vec_init(len);
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if (acb_is_one(a))
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acb_dirichlet_zeta_jet(t, h, deflate, len, prec);
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else
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_acb_poly_zeta_cpx_series(t, h, a, deflate, len, prec);
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/* compose with nonconstant part */
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acb_zero(u);
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_acb_vec_set(u + 1, h + 1, hlen - 1);
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_acb_poly_compose_series(res, t, len, u, hlen, len, prec);
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_acb_vec_clear(t, len);
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_acb_vec_clear(u, len);
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}
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void
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acb_poly_zeta_series(acb_poly_t res, const acb_poly_t f, const acb_t a, int deflate, slong n, slong prec)
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{
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if (n == 0)
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{
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acb_poly_zero(res);
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return;
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}
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acb_poly_fit_length(res, n);
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if (f->length == 0)
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{
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acb_t t;
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acb_init(t);
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_acb_poly_zeta_series(res->coeffs, t, 1, a, deflate, n, prec);
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acb_clear(t);
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}
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else
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{
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_acb_poly_zeta_series(res->coeffs, f->coeffs, f->length, a, deflate, n, prec);
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}
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_acb_poly_set_length(res, n);
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_acb_poly_normalise(res);
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}
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